The quantifier-elimination tag has no wiki summary.
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1answer
73 views
Herbrand Logic-Fitch System
Given $$\forall x.(p(x) \implies q(x))\quad and \quad p(a)$$ use the Fitch system to prove q(a)
I have started:
$$\\$$
$$1) \forall X.(p(X) \implies q(X)) \qquad (Premise)$$
$$2) p(a) \qquad ...
1
vote
1answer
54 views
Proof of Robinson's test
I have been working with Tent and Ziegler's Model Theory.
I am on the Quantifier elimination chapter, and there they mention Robinson's test. It says that, for an $L$-theory $T$ three statements ...
3
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1answer
68 views
Quantifier Elimintion of $(\Bbb{Q},+,0)$
I want to prove that the structure $(\Bbb{Q},+,0)$ has Quantifier Elimination.
I can prove it for some simple basic formulas, but what if i get a formula which says that i have a linear combination, ...
2
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1answer
115 views
How to prove that something is definable or not definable in a given structure?!
Hello friends of mathematics :)
I have some problems with the topic "Is something definable in a structure". I can solve some problems for example the following questions:
Is the relation definable ...
4
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3answers
98 views
Want to show Quantifier elimination and completeness of this set of axioms…
Let $\Sigma_\infty$ be a set of axioms in the language $\{\sim\}$ (where $\sim$ is a binary relation
symbol) that states:
(i) $\sim$ is an equivalence relation;
(ii) every equivalence ...
2
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1answer
42 views
Need a FOL derivation validated. Unclear on universal generalization restriction.
I'm currently working through Suppes' Introduction to Logic, and while the text is excellent, the lack of solutions to the exercises can be frustrating at times. This is one of those times. I've ...
2
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1answer
123 views
Reducing quantification to probability
I was thinking about some problem involving quantifiers (the existencial and universal quantifiers) and I noticed how it might resemble probability in a sense. They both assume a variable and its ...
10
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2answers
587 views
Software for solving geometry questions
When I used to compete in Olympiad Competitions back in high school, a decent number of the easier geometry questions were solvable by what we called a geometry bash. Basically, you'd label every ...
