An algebraic and Kripke-style approach to a certain extension of intuitionistic logic

Cecylia Rauszer

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1980

Abstract

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CONTENTSIntroduction............................................................................... 5Chapter I. Semi-Boolean algebras 1. Semi-Boolean algebras....................................... 8 2. Q-filters in semi-Boolean algebras............................ 11 3. Extensions of semi-Boolean algebras...................... 15Chapter II. Algebraic and semantic modelsfor Heyting-Brouwer logic 1. Preliminaries.......................................................... 17 2. Algebraic structures....................................................... 21 3. Completeness theorems............................................. 23 4. Deduction theorems...................................................... 24 5. Saturated H-B theories................................................. 26 6. Craig interpolation lemma........................................... 29 7. Theory of falsity............................................................... 31 8. Kripke-style models....................................................... 34 9. Canonical structures..................................................... 39 10. Connections between a-models and k-models.... 42Chapter III. Model theory for Heyting-Brouwer logic 1. Ultraproducts.......................................................... 45 2. Model extension theorem............................................. 47 3. Connections between H-B logic and DI logic........... 56References....................................................................................... 59List of symbols................................................................................. 60List of definitions............................................................................. 61

How to cite

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Cecylia Rauszer. An algebraic and Kripke-style approach to a certain extension of intuitionistic logic. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1980. <http://eudml.org/doc/268511>.

@book{CecyliaRauszer1980,
abstract = {CONTENTSIntroduction............................................................................... 5Chapter I. Semi-Boolean algebras 1. Semi-Boolean algebras....................................... 8 2. Q-filters in semi-Boolean algebras............................ 11 3. Extensions of semi-Boolean algebras...................... 15Chapter II. Algebraic and semantic modelsfor Heyting-Brouwer logic 1. Preliminaries.......................................................... 17 2. Algebraic structures....................................................... 21 3. Completeness theorems............................................. 23 4. Deduction theorems...................................................... 24 5. Saturated H-B theories................................................. 26 6. Craig interpolation lemma........................................... 29 7. Theory of falsity............................................................... 31 8. Kripke-style models....................................................... 34 9. Canonical structures..................................................... 39 10. Connections between a-models and k-models.... 42Chapter III. Model theory for Heyting-Brouwer logic 1. Ultraproducts.......................................................... 45 2. Model extension theorem............................................. 47 3. Connections between H-B logic and DI logic........... 56References....................................................................................... 59List of symbols................................................................................. 60List of definitions............................................................................. 61},
author = {Cecylia Rauszer},
keywords = {intuitionistic sentential calculus; Kripke-style semantics; algebraic study of semi-Boolean algebras; extension of the intuitionistic predicate calculus; logic of constant domains; conservative extension},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {An algebraic and Kripke-style approach to a certain extension of intuitionistic logic},
url = {http://eudml.org/doc/268511},
year = {1980},
}

TY - BOOK
AU - Cecylia Rauszer
TI - An algebraic and Kripke-style approach to a certain extension of intuitionistic logic
PY - 1980
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction............................................................................... 5Chapter I. Semi-Boolean algebras 1. Semi-Boolean algebras....................................... 8 2. Q-filters in semi-Boolean algebras............................ 11 3. Extensions of semi-Boolean algebras...................... 15Chapter II. Algebraic and semantic modelsfor Heyting-Brouwer logic 1. Preliminaries.......................................................... 17 2. Algebraic structures....................................................... 21 3. Completeness theorems............................................. 23 4. Deduction theorems...................................................... 24 5. Saturated H-B theories................................................. 26 6. Craig interpolation lemma........................................... 29 7. Theory of falsity............................................................... 31 8. Kripke-style models....................................................... 34 9. Canonical structures..................................................... 39 10. Connections between a-models and k-models.... 42Chapter III. Model theory for Heyting-Brouwer logic 1. Ultraproducts.......................................................... 45 2. Model extension theorem............................................. 47 3. Connections between H-B logic and DI logic........... 56References....................................................................................... 59List of symbols................................................................................. 60List of definitions............................................................................. 61
LA - eng
KW - intuitionistic sentential calculus; Kripke-style semantics; algebraic study of semi-Boolean algebras; extension of the intuitionistic predicate calculus; logic of constant domains; conservative extension
UR - http://eudml.org/doc/268511
ER -

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