Add to ORKGIntroduction This short note presents two simple applications of the notion of boolean models for first-order classical logic. One application is a constructive proof of the following conservativity result: if a first-order theory T proves a formula 8x9y OE(x; y) then the theory T 0 which is T extended with a new function symbol f and the axiom 8x OE(x; f(x)) is conservative over T . There is a short proof of this fact using the completeness theorem and the axiom of choice. By the axiom of choice, any model of T can be extended to a model of T 0 : Hence, if / is a formula which does not mention f; this formula holds in all models of T if it holds in all models of T
We define a weak second--order extension of first--order logic. We prove a second--order cut elimina...
Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper s...
We give two characterizations of conservative extensions of models of arithmetic, in terms of the ex...
A Boolean algebra is a structure which behaves very much like first order propositional logic. In th...
In this paper we will present a definability theorem for first order logic This theorem is very easy...
In this paper we will present a definability theorem for first order logic This theorem is very easy...
We define a notion of logic that provides a general framework for the study of extensions of first-o...
Boolean valued structures are defined and some of their properties are studied. Completeness and com...
Boolean valued structures are defined and some of their properties are studied. Completeness and com...
In this paper, we will present a definability theorem for first order logic.This theorem is very eas...
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus...
In this paper, we give two fairly simple models of set theory with the unrestricted comprehension ba...
In this paper, we give two fairly simple models of set theory with the unrestricted comprehension ba...
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus...
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus...
We define a weak second--order extension of first--order logic. We prove a second--order cut elimina...
Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper s...
We give two characterizations of conservative extensions of models of arithmetic, in terms of the ex...
A Boolean algebra is a structure which behaves very much like first order propositional logic. In th...
In this paper we will present a definability theorem for first order logic This theorem is very easy...
In this paper we will present a definability theorem for first order logic This theorem is very easy...
We define a notion of logic that provides a general framework for the study of extensions of first-o...
Boolean valued structures are defined and some of their properties are studied. Completeness and com...
Boolean valued structures are defined and some of their properties are studied. Completeness and com...
In this paper, we will present a definability theorem for first order logic.This theorem is very eas...
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus...
In this paper, we give two fairly simple models of set theory with the unrestricted comprehension ba...
In this paper, we give two fairly simple models of set theory with the unrestricted comprehension ba...
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus...
This textbook provides a concise and self-contained introduction to mathematical logic, with a focus...
We define a weak second--order extension of first--order logic. We prove a second--order cut elimina...
Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper s...
We give two characterizations of conservative extensions of models of arithmetic, in terms of the ex...