Large cardinals and the Continuum Hypothesis
... decides CH one way or the other? In fact there are many of these, such as MA or PFA,2 but we will require ϕ to be one of a more special kind. In 1946, that is well before the development of forcing, Gödel entertained the idea of so called stronger axioms of infinity deciding CH (and other independ ...
... decides CH one way or the other? In fact there are many of these, such as MA or PFA,2 but we will require ϕ to be one of a more special kind. In 1946, that is well before the development of forcing, Gödel entertained the idea of so called stronger axioms of infinity deciding CH (and other independ ...
Gödel Without (Too Many) Tears
... Gödel’s doctoral dissertation, written when he was 23, established the completeness theorem for the first-order predicate calculus (i.e. a standard proof system for first-order logic indeed captures all the semantically valid inferences). Later he would do immensely important work on set theory, as ...
... Gödel’s doctoral dissertation, written when he was 23, established the completeness theorem for the first-order predicate calculus (i.e. a standard proof system for first-order logic indeed captures all the semantically valid inferences). Later he would do immensely important work on set theory, as ...
The substitutional theory of logical consequence
... For formalized languages the substitutional account of logical validity has largely been superseded by the proof-theoretic and the model-theoretic approaches. According to the proof-theoretic or inferentialist conception, roughly, an argument is valid if and only if the conclusion can be derived fro ...
... For formalized languages the substitutional account of logical validity has largely been superseded by the proof-theoretic and the model-theoretic approaches. According to the proof-theoretic or inferentialist conception, roughly, an argument is valid if and only if the conclusion can be derived fro ...
First-Order Intuitionistic Logic with Decidable Propositional
... their subsets”. Propositional logic can be considered a part of the mathematics of finite sets because of availability of finite models using truth tables. Thus, LEM for propositional formulas is not really a target of intuitionistic criticism of classical logic. The classical assumption that every ...
... their subsets”. Propositional logic can be considered a part of the mathematics of finite sets because of availability of finite models using truth tables. Thus, LEM for propositional formulas is not really a target of intuitionistic criticism of classical logic. The classical assumption that every ...
slides
... If there are infinitely many possible values for X the meaning of this expression cannot be represented using a propositional formula. In AG, the meaning of aggregate expressions is captured using an infinitary propositional formula. The definition is based on the semantics for propositional aggrega ...
... If there are infinitely many possible values for X the meaning of this expression cannot be represented using a propositional formula. In AG, the meaning of aggregate expressions is captured using an infinitary propositional formula. The definition is based on the semantics for propositional aggrega ...