{"result":[{"biographic_references":[],"contributors":{"authors":[{"aliases":[],"checked":"1","codes":["macintyre.angus-j"],"name":"Macintyre, Angus"},{"aliases":[],"checked":"1","codes":["wilkie.alex-j"],"name":"Wilkie, A. J."}],"author_references":[],"editors":[]},"database":"Zbl","datestamp":"0001-01-01T00:00:00Z","document_type":{"code":"a","description":"serial article"},"editorial_contributions":[{"language":"English","reviewer":{"author_code":"peckhaus.volker","reviewer_id":"7784","name":"Volker Peckhaus","sign":"V.Peckhaus (Erlangen)"},"text":"The authors discuss the ``two structures \\(\\langle\\overline{\\mathbb R}, \\exp\\rangle\\) and \\(\\langle \\overline {\\mathbb R}, e\\rangle\\), where \\(\\overline {\\mathbb R}= \\langle {\\mathbb R},+,\\cdot, -, 0, 1, <\\rangle\\) denotes the ordered field of real numbers (in the language of ordered rings), exp : \\( {\\mathbb R} \\rightarrow {\\mathbb R}\\) is the usual exponential function and \\(e\\) : \\({\\mathbb R}\\rightarrow{\\mathbb R}, x \\mapsto \\text{ exp}((1 + x^2)^{-1})\\) is the \\textit{restricted} exponential function [\\dots]'' (p. 441). The theories of these structures are denoted by \\(T_{\\text{exp}}\\) and \\(T_e\\). The decidability of \\(T_{\\text{exp}}\\) is finally proved. Good knowledge of Wilkie's paper on model completeness of \\(T_{\\text{exp}}\\) and \\(T_e\\) [\\textit{A. J. Wilkie}, J. Am. Math. Soc. 9, No. 4, 1051-1094 (1996; Zbl 0892.03013)] is required.\n\nFor the entire collection see [Zbl 0894.03002].","contribution_type":"review"}],"id":1169378,"identifier":"0896.03012","keywords":["decidability","real exponential field"],"language":{"languages":["English"],"addition":[null]},"license":[],"links":[],"msc":[{"code":"03B25","scheme":"msc2020","text":"Decidability of theories and sets of sentences"},{"code":"12L05","scheme":"msc2020","text":"Decidability and field theory"},{"code":"03C62","scheme":"msc2020","text":"Models of arithmetic and set theory"},{"code":"03C35","scheme":"msc2020","text":"Categoricity and completeness of theories"},{"code":"12L12","scheme":"msc2020","text":"Model theory of fields"}],"references":[],"source":{"book":[{"book_id":981114,"isbn":[{"number":"1-56881-061-X","type":"hbk"}],"publisher":"Wellesley, MA: A K Peters","year":"1996"}],"pages":"441-467","series":[],"source":"Odifreddi, Piergiorgio (ed.), Kreiseliana: about and around Georg Kreisel. Wellesley, MA: A K Peters. 441-467 (1996)."},"states":[["c","is cited"]],"title":{"addition":null,"original":null,"subtitle":null,"title":"On the decidability of the real exponential field"},"year":"1996","zbmath_url":"https://zbmath.org/1169378"}],"status":{"execution":"successful request","execution_bool":true,"internal_code":"ok","last_id":null,"nr_total_results":1,"nr_request_results":1,"query_execution_time_in_seconds":0.07803678512573242,"status_code":200,"time_stamp":"2026-10-22T13:11:34Z"}}