We consider equational theories for functions defined via recursion involving equations between closed terms with natural rules based on recursive definitions of the function symb...
Modifying the methods of Z. Adamowicz's paper Herbrand consistency and bounded arithmetic (Fund. Math. 171 (2002)), we show that there exists a number n such that m Sm (the u...
Devising an efficient deterministic – or even a nondeterministic sub-exponential time – algorithm for testing polynomial identities is a fundamental problem in algebraic comp...
We study the problem of proving in weak theories of Bounded Arithmetic the theorem that there are arbitrarily large prime numbers. We show that the theorem can be proved by some &...
We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmeti...