{'fraction_non_alphanumeric': 0.019969278033794162, 'fraction_numerical': 0.009216589861751152, 'mean_word_length': 4.927272727272728, '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}}
A note on bootstrapping intuitionistic bounded arithmetic

This paper, firstly, discusses the relationship between Buss’s definition and Cook and Urquhart’s definition of BASIC axioms and of IS 2 . The two definitions of BASIC axioms are not equivalent; however, each intuitionistically implies the law of the excluded middle for quantifier-free formulas. There is an elementary proof that the definitions of IS 2 are equivalent which is not based on realizability or functional interpretations. Secondly, it is shown that any negated positive consequence of S 2 is also a theorem of IS 2 . Some possible additional axioms for IS 1 2 are investigated.