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The first‐order theory of raising to an infinite power
Author(s) -
Foster Tom
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq056
Subject(s) - decidability , mathematics , exponent , exponential function , order (exchange) , function (biology) , field (mathematics) , model theory , raising (metalworking) , power (physics) , discrete mathematics , pure mathematics , calculus (dental) , mathematical analysis , geometry , quantum mechanics , medicine , physics , dentistry , finance , economics , philosophy , linguistics , evolutionary biology , biology
We introduce a first‐order theory T ∞ which can be seen as the theory of certain real closed fields, each expanded by a power function with infinite exponent. We prove that T ∞ is model‐complete and is decidable if and only if the theory of the real field with the exponential function is decidable.