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oai:www.ideals.illinois.edu:2142/115816 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Hieronymi, Philipp 2022-05 application/pdf en text Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-14 without embargo terms The student, Xiaoduo Wang, accepted the attached license on 2022-04-19 at 13:10. The student, Xiaoduo Wang, submitted this Thesis for approval on 2022-04-19 at 13:17. This Thesis was approved for publication on 2022-04-26 at 14:57. DSpace SAF Submission Ingestion Package generated from Vireo submission #17804 on 2022-11-14 at 17:33:55 Quantifier elimination and decidability of the theory of additive integer group augmented by predicates of multiplicative cyclic submonoids Wang, Xiaoduo 2022-04-26 Model Theory Logic Number Theory In this thesis, we study an extension of the theory of the additive group of integers. To be more specific, if we let {q1, q2, ...} be an enumeration of all positive prime integers and for each positive prime integers q, let qN denote the set {qn : n ∈ N}, then we are interested in the theory Th(Z,+,−, 0, 1, qNi )i∈I, where I ⊆ N. We give a set of sentences T explicitly and show that T axiomatizes the theory using a back-and-forth system. We also investigate the extent of quantifier elimination of T and its decidability. In particular, we show that every formula in the language of groups is T-equivalent to a boolean combination of existential formulas, and we also show that the decidability of Th(Z,+,−, 0, 1, qNi )i∈I is equivalent to a number theoretical problem. Thesis eng https://hdl.handle.net/2142/115816 Copyright 2022 Xiaoduo Wang M.S. Thesis Mathematics University of Illinois at Urbana-Champaign Mathematics