This question is from course Advanced Logic in graduate level.Please give the answer, if yoy know, in a clear and understandable way, as soon as you can. 5. A set of formulas Mo is an axiom system for a set of formulas M if{A A is a model for Mo} = {A | A is a model for M}M is called finitely axiomatizable if it has a finite axiom system. Suppose {F1, F2, F3,...} is an axiom systemfor a set M where for all n ≥ 1, = Fn+1 → Fn and FnFn+1. Show that M is not finitely axiomatizable.

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Answered: 5. A set of formulas Mo is an axiom…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

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This question is from course Advanced Logic in graduate level. Please give the answer, if yoy know, in a clear and understandable way, as soon as you can.

5. A set of formulas Mo is an axiom system for a set of formulas M if
{A A is a model for Mo} = {A | A is a model for M}
M is called finitely axiomatizable if it has a finite axiom system. Suppose {F1, F2, F3,...} is an axiom system
for a set M where for all n ≥ 1, = Fn+1 → Fn and FnFn+1. Show that M is not finitely axiomatizable.

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in the solution it says "Now, consider the model that satisfies all axioms in {A1, A2, ..., Ak} (since it's finite, it can be satisfied by a model), but also satisfies Fm because Fm implies Fm+1" but it is given that Fm doesnot imply fm+1

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