{'fraction_non_alphanumeric': 0.03434739941118744, 'fraction_numerical': 0.011776251226692836, 'mean_word_length': 4.862068965517241, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Imaginaries in algebraically closed valued fields

These notes are intended to accompany the tutorial series ‘Model theory of algebraically closed valued fields’ in the Workshop ‘An introduction to recent applications of model theory’, Cambridge March 29–April 8, 2005. They do not contain any new results, except for a slightly new method of exposition, due to Lippel, of parts of the proof of elimination of imaginaries, in Sections 8 and 9. They form an exposition of [4], and, much more briefly, [5]. These papers are also surveyed in [6]. The plan of the tutorial series is as follows: the first lecture and a half will be devoted to background on algebraically closed valued fields, the meaning of ‘elimination of imaginaries’, with examples, and description of the sorts in which algebraically closed valued fields eliminate imaginaries. The next two and a half lectures will be devoted to (parts of) the proof of this theorem. The final session will be on stable domination and orthogonality to the value group.