Computability Theory and Foundations of Mathematics
نویسندگان
چکیده
منابع مشابه
Foundations of Mathematics in the Twentieth Century
1. INTRODUCTION AND EARLY DEVELOPMENTS. Logic and foundations are a domain of mathematics concerned with basic mathematical structures (in terms of which one can define all other mathematical structures), with the correctness and significance of mathematical reasoning, and with the effectiveness of mathematical computations. In the twentieth century, these areas have crystallized into three lar...
متن کاملComputability Theory
0. INTRODUCTION. Computability is perhaps the most significant and distinctive notion modern logic has introduced; in the guise of decidability and effective calculability it has a venerable history within philosophy and mathematics. Now it is also the basic theoretical concept for computer science, artificial intelligence and cognitive science. This essay discusses, at its heart, methodologica...
متن کاملComputable Model Theory
Computability theory formalizes the intuitive concepts of computation and information content. Pure computability studies these notions and how they relate to definability in arithmetic and set theory. Applied computability examines other areas of mathematics through the lens of effective processes. Tools from computability can be used to give precise definitions of concepts such as randomness....
متن کاملComputational Complexity of Boolean Formulas with Query Symbols
03D15 (Mathematical logic and foundations / Recursion theory / Complexity of computation), 03E40 (Mathematical logic and foundations / Set theory / Other aspects of forcing and Boolean-valued models), 68Q15 (Computer science / Theory of computing / Complexity classes).
متن کاملThe Significance of Aristotle's Particularisation in the Foundations of Mathematics, Logic and Computability: Rosser and Formally Undecidable Arithmetical Propositions
The logic underlying our current interpretations of all first-order formal languages—which provide the formal foundations for all computing languages—is Aristotle’s logic of predicates. I review Rosser’s claim that Gödel’s reasoning can be recast to arrive at his intended result without the assumption of ω-consistency, since Rosser’s argument appeals to a fundamental tenet of this logic, namely...
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تاریخ انتشار 2014