A Note on Omitting Types in Propositional Logic
نویسندگان
چکیده
Analogues of the classical omitting types theorems of first-order logic are proved for propositional logic. For an infinite cardinal κ, a sufficient criterion is given for the omission of κ-many types in a propositional language with κ propositional variables.
منابع مشابه
Equality propositional logic and its extensions
We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...
متن کاملTruth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملSemantics of intuitionistic propositional logic
Intuitionistic logic is a weakening of classical logic by omitting, most prominently, the principle of excluded middle and the reductio ad absurdum rule. As a consequence, this logic has a wider range of semantical interpretations. The motivating semantics is the so called Brouwer-Heyting-Kolmogorov interpretation of logic. The propositions A,B,C, . . . are regarded as problems or tasks to be s...
متن کاملOmitting Types: Application to Descriptive Set Theory
The omitting types theorem of infinitary logic is used to prove that every small II set of analysis or any small 2. set of set theory is constructible. In what follows we could use either the omitting types theorem for infinitary logic or the same theorem for what Grilliot[2] calls (eA)-logic. I find the latter more appealing. Suppose i_ is a finitary logical language containing the symbols of ...
متن کاملAn Omitting Types Theorem for Finite Schematizable Algebraic Logic
We prove an Omitting Types Theorem for the extension of first order logic studied by Németi, Sain and others as a solution to the so-called Finitization Problem in Algebraic Logic. A new omitting types theorem for first order logic is obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015