I'm doing my undergraduate dissertation on axiomatic set theory, and i'm using Jean-Louis Krivine's book "Theorie des ensembles" as a reference book. My dissertation focuses only on the first two chapters " zermelo fraenkel set theory " and " cardinals and ordinals ". And i'm searhing for some references to help me write the introduction to my dissertation.  Any help would be much appreciated.
I want to do a survey of textbooks in set theory. Amazon returns 3582 books for the keywords "set theory". A small somewhat random selection with number of references in Google scholar is the following.   Two questions:    What textbooks in set-theory are considered standard?  What is a good place to aggregate standard references (of textbooks)?    (I'm only interested in text-books, which as a format already provide a kind of standardization)  Textbooks on set theory (author: title (year) #Google Scholar citations )   Thomas J. Jech: Set Theory 3rd Edition (1978) #2441  Kenneth Kunen: Set Theory (1980) #1881  P. R. Halmos: Naive Set Theory (1974) #1079 AA Fraenkel, Y Bar-Hillel, A Levy: Foundations of set theory (1973) #696 K Kuratowski, A Mostowski, M Mączyński: Set theory (1976) #609 Suppes: Axiomatic set theory  (1972) #589 Quine: Set theory and its logic (1969) #442 A Levy: Basic set theory (1979) #442 Herbert B. Enderton: Elements of Set Theory (1977) #349 Karel Hrbacek, Thomas J. Jech: Introduction to set theory (1999) #284 RR Stoll: Set theory and logic (1979) #281  N. Bourbaki: theory of sets (1970) #211 K Devlin: The joy of sets: fundamentals of contemporary set theory (1994) #182 Ciesielski: Set theory for the working mathematician (1997) #156 YN Moschovakis: Notes on set theory (1994) #138 FW Lawvere: Sets for mathematics (2003) #118 G Takeuti, WM Zaring: Introduction to axiomatic set theory (1982) #106 Kaplansky: Set Theory and Metric Spaces (2001) #103 Potter: Set Theory and Its Philosophy: A Critical Introduction (2004) #91 PT Johnstone: Notes on logic and set theory (1987) #87 Judith Roitman: Introduction to Modern Set Theory (1990) #47 Derek Goldrei: Set Theory: For Guided Independent Study (1996) #31 Basic set theory: A Shen, NK Vereshchagin (2002) #14 Ralf Schindler: Set Theory (2014) #13 Foreman, Kanamori: Handbook of Set Theory (2009) #38   Note:  Please feel free to add textbooks to the list, as long as they are not just on a smaller subset of set theory. (Some of the dates might not be the first published edition.)
Who were the other two heroes with Superman in the newspaper article who left? In Justice League, we see a newspaper article showing three heroes who died (left to their home planets) but it was too fast that I missed catching the faces.   Who were the other two heroes who are dead? What is Java's answer to WPF? If a stock doesn't pay dividends, then why is the stock worth anything? I read somewhere that companies are not required to pay dividends to shareholders (this is correct, yes?).   If so, then if company A never pays dividends to its shareholders, then what is the point of owning company A's stock? Surely the right to one vote for company A's Board can't be that valuable.   What is it that I'm missing? I am new to photography, and need a little advice. I currently have a .   To get rolling, where do I go from here? Does the camera matter? Is this camera enough to start with? "Now" vs "by now" Consider these examples:   By now the desk should be looking significantly tidier!  By now, the failure of regulators to contain dangerous forces should be well accepted.  By now I own some forty copies of the magazine.  By now the blue of twilight is glowing.  He used leverage, but by now applied concerted discipline to contain his risks.    I wonder if I can use &quot;now&quot; instead of &quot;by now&quot; to convey the same meaning. I would think &quot;by now&quot; refers to a moment until now, but why not use past tense or present perfect tense in the these examples? I'm trying to create an annotated bibliography. Here's my .tex document:  \documentclass[12pt]{article} \title{Annotated Bibliography}  \begin{document}  \nocite{*}  \bibliography{annotatedbib}  \end{document}   And here is the associated .bib document:  @Misc{hacker,     AUTHOR = `{Andrew Hacker'},     TITLE = {Is Algebra Necessary?},     HOWPUBLISHED = {New York Times},     MONTH = {July 31},     YEAR = {2012},     ANNOTE = {This article was published in the New York Times.}, }   No matter into which format I compile my .tex document, the annotation will not show up! Is there something that I'm missing? I am making a fudge recipe that calls for 1cup whole milk and 5 cups sugar. It also uses 2 sticks of butter and 25 marshmallows. I'm wondering if I can omit the milk and cut back on the sugar by using sweetened condensed milk. How do I use the Tooling API to create a new Apex Trigger? How do I use the Tooling API to create a new Apex Trigger (rather than update an existing one)?  According to the  I need to specify the ContentEntityId as an existing Trigger Id. But in my case I don't have an Id because I've trying to create a new sObject.  If I omit the ContentEntityId I get an error back in the SaveResult:     Status Code: INSUFFICIENT_ACCESS_ON_CROSS_REFERENCE_ENTITY   Message: "insufficient access rights on cross-reference id"   The following is more or less a test case in C# that attempts to use the SOAP tooling API to create the new trigger.  SforceService toolingService = //... Get instance of the Tooling API  MetadataContainer container = new MetadataContainer(); container.Name = "Test" + DateTime.Now.Ticks;  SaveResult[] saveResult = toolingService.create(new sObject[] { container }); string metaDataContainerId = saveResult[0].id;  ApexTriggerMember apexTriggerMember = new ApexTriggerMember(); apexTriggerMember.MetadataContainerId = metaDataContainerId; apexTriggerMember.Body = "trigger TestOpportunityBeforeUpdate on Opportunity (before update) {\n//Horray\n}";     // Adding this will successfuly update the existing trigger //apexTriggerMember.ContentEntityId = "01q70000000GuzP";  SaveResult[] triggerSaveResults = toolingService.create(new sObject[] { apexTriggerMember }); Assert.AreEqual(1, triggerSaveResults.Length); SaveResult triggerSaveResult = triggerSaveResults[0]; if (!triggerSaveResult.success) {     Assert.Fail(triggerSaveResult.errors[0].message); } Assert.IsTrue(triggerSaveResult.success);  ContainerAsyncRequest containerRequest = new ContainerAsyncRequest(); containerRequest.MetadataContainerId = metaDataContainerId; containerRequest.IsCheckOnly = false;  SaveResult[] containerResults = toolingService.create(new sObject[] { containerRequest }); In a USB cable, is it OK to swap the D+ and D- wires? I heard that D+ and D- are differential signals, does it matter if I swap them when connecting a USB device to the computer? Having trouble creating an array of objects The answer is, according to the book: $(m-1)!\cdot \binom{m+r-1}{r}$ I get why this is true. You arrange $m$ people in their seats in $(m-1)!$ ways and then you put $r$ empty spots inbetween them.I was thinking - choose $m$ seats out of $m+r$ to put the people on => $\binom{m+r}{m}$ Arrange them once you've chosen the seats $\to (m-1)!$ So in total: $\binom{m+r}{m} \cdot (m-1)!$ This is obviously not true. What's wrong with the way I'm thinking? Enumerate paragraphs and subparagraphs like sections but with letters I'm using pandoc and in my template.tex exists this code to make the paragraphs and subparagraphs to behave like sections.  % Redefines (sub)paragraphs to behave more like sections \ifx\paragraph\undefined\else \let\oldparagraph\paragraph \renewcommand{\paragraph}[1]{\oldparagraph{#1}\mbox{}} \fi \ifx\subparagraph\undefined\else \let\oldsubparagraph\subparagraph \renewcommand{\subparagraph}[1]{\oldsubparagraph{#1}\mbox{}} \fi   This code generate number like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.1 paragraph  1.1.1.1.1.1 subparagraph   How to change this code to enumerate with letter like this:  1. chapter  1.1 section  1.1.1 subsection  1.1.1.1 subsubsection  1.1.1.1.a paragraph  1.1.1.1.a.a subparagraph How can I select a point without selecting its reflected side Schengen Visa four years- 90 days stay I have been granted multiple entry Schengen Visa valid for 4 years with the duration of stay of 90 days. Does it mean only 90 days of stay in total during a 4 years period?  I'll be travelling to Schengen Area in September for 25 days, then after 2 month or so I will travel again for 30 days. Similarly, I'll be traveling to the Schengen Area in the future depending on the business meetings.  How will I know, that how many days are left? On what basis the calculations are done?  Also, please explain the "90/180" rule. How to secure database passwords in PHP? When a PHP application makes a database connection it of course generally needs to pass a login and password. If I'm using a single, minimum-permission login for my application, then the PHP needs to know that login and password somewhere. What is the best way to secure that password? It seems like just writing it in the PHP code isn't a good idea. Is my way of solving and my answer correct?  Let $f(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\frac{x^4}{4}+\frac{x^5}{5}$   And $g(x)=f^{-1}(x)$  Find $g'''(0)$  My attempt:  We know that $g'(x)=\frac{1}{f'(g(x))}$  $f'(x)=1+x+x^2+x^3+x^4=\frac{x^5-1}{x-1}$  $f'(g(x))=\frac{(g(x))^5-1}{(g(x))-1}$  $\Rightarrow g'(x)=\frac{(g(x))-1}{(g(x))^5-1}$  $\Rightarrow g'(x)[(g(x))^5-1]=g(x)-1$  Similarly differentiating again,  $\Rightarrow g'(x)[5(g(x))^4]+[(g(x))^5-1]g''(x)=g'(x)$  Similarly differentiating again,  $\Rightarrow g'(x)[20(g(x))^3g'(x)]+[5(g(x))^4]g''(x)+[(g(x))^5-1]g'''(x)+g''(x)[5(g(x))^4]=g''(x)$  Putting $x=0$,  $g(0)=f^{-1}(0)=0$  $g'(0)=\frac{1}{f'(g(0))}=\frac{1}{f'(0)}=1$  similarly,$g''(0)=-1$  $\Rightarrow g'''(0)=1$ Prove that $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$   My proof is below. I am interested in other proofs.    My proof  Let   $$f (\mathrm X) := \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B)$$  Hence,  $$\begin{array}{rl} f (\mathrm X + h \mathrm V) &amp;= \mbox{tr} (\mathrm A (\mathrm X + h \mathrm V)^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A (\mathrm X ( \mathrm I + h \mathrm X^{-1} \mathrm V))^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I + h \mathrm X^{-1} \mathrm V)^{-1} \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I - h \mathrm X^{-1} \mathrm V + O (h^2)) \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) - h \, \mbox{tr} ( \mathrm A \mathrm X^{-1} \mathrm V \mathrm X^{-1} \mathrm B) + O (h^2)\\ &amp;= f (\mathrm X) - h \, \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) + O (h^2)\end{array}$$  Thus, the directional derivative of $f$ in the direction of $\mathrm V$ at $\mathrm X$ is  $$D_{\mathrm V} f (\mathrm X) = - \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) = - \mbox{tr} ( (\mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top})^\top \mathrm V ) = - \langle \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}, \mathrm V \rangle$$  and, lastly,  $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$ When I wake up and do stretching I hear some sounds from my joints. What do you call this crunching sound from bone joints? Frea is trying to kill me I've been trying to play the Dragonborn DLC for Skyrim on the PS3. In order to advance the story, I need to talk to Frea and her dad. But every time I go near the village they try and murder me for slaughtering the village back when I was like level 15 (I'm level 43 now).  I've tried yielding but they won't accept it and I don't know how to make them stop, all I want to do is finish the story. Does anybody know how to fix this issue? I have two screens on my Windows 8.1 computer (with Classic Shell Start Menu installed). The thing is that I would like to have the taskbar's  (where the clock and all the icons like Skype or Spotify are, at the right) on both of my screens, and not only on the primary one.  Could you help me ? I would like not to install a heavy and paid software like DisplayFusion.