{'fraction_non_alphanumeric': 0.03748326639892905, 'fraction_numerical': 0.019410977242302542, 'mean_word_length': 4.245614035087719, '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': 2, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Chevalley groups over fields and their elementary properties

Two models U and B of a (ﬁrst-order) language L are said to be elementarily equivalent if any statement ϕ in L is satisﬁed in the model U if and only if it is satisﬁed in the model B . Questions concerning the elementary equivalence of linear groups were ﬁrst considered by Mal’tsev in 1961. He proved the following structure theorem in [1]: The groups G m ( K 1 ) and G n ( K 2 ) ( G = GL , PGL , SL , PSL , m (cid:2) n (cid:2) 3, and K 1 , K 2 are ﬁelds of characteristic 0) are elementarily equivalent if and only if m = n and K 1 and K 2 are elementarily equivalent . This theory received an extension in 1992, when progress in model theory enabled Beidar and Mikhalev to propose in [2] a general method of solving problems of this type. Using an ultraproductconstruction and the Keisler–Shelah isomorphism theorem (see [3]), they generalized Mal’tsev’s theorem to the case of the group GL over a prime associative ring containing 1 / 2 or over a ﬁeld. In 2001 (see [4]) the author studied the elementary properties of Chevalley groups over alge-braically closed ﬁelds of characteristic diﬀerent from two. In this paper the results of [4] are extended to Chevalley groups over inﬁnite ﬁelds of characteristic diﬀerent from two. We do not consider ﬁnite ﬁelds, because two ﬁnite models of the same language are elementarily equivalent if and only if they are isomorphic. main results of this paper are the following two theorems.