# Tagged Questions

Questions about mathematical logic, including model theory, proof theory, computability theory (a.k.a. recursion theory), and non-standard logics. Questions which merely seek to apply logical or formal reasoning to other areas of mathematics should not use this tag. Consider using one of the ...

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### An easy example of a non-constructive proof without an obvious “fix”?

I wanted to give an easy example of a non-constructive proof, or, more precisely, of a proof which states that an object exists, but gives no obvious recipe to create/find it. Euclid's proof of the ...
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### What is the difference between weak and strong completeness in many valued logic?

I know a bunch of facts about weak and strong completeness in many valued logic, that there is strong completeness for the finite mv logic, and that for the infinite ones you can either only have weak ...
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### Can someone verify my assertion from this english sentence? [duplicate]

This is from Discrete Mathematics and its Applications This is the book means when mentions a list of common ways to express conditional statements After going through the list, I immediately ...
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### Clarifying on how if p,q is logically equivalent to p only if q [duplicate]

Here is what my book says about the different ways implications are worded I am struggling with how "if p, then q" is logically equivalent to "p only if q" The example I came up with With "if p,...
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### How to tell the difference between interval and coordinate notation from context?

I am working on a practice problem with sets. (the answer key) At first I was confused by the notation Ai = (0,i), i is a natural number. I looked up the use of paranthesis and saw that they could ...
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In the literature on Description Logic, when interpretations are explained, we encounter expressions like, $$\mathcal{I} = (\Delta^\mathcal{I}, \cdot^\mathcal{I})$$ (Actually, I am talking about, ...
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### How to adapt proof by contradiction showing that a sqrt(2) is irrational for sqrt(20)?

This example is from Discrete Math and its Applications I understand the steps the author is taking. First he assumes sqrt(2) is rational meaning that there exists integers a, and b such that ...
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### Discrete Math - Determine truth value of each proposition

If 3 + 5 < 2, then 1 + 3 $\neq$ 4 Can someone kindly check my work? Let p: 3 + 5 < 2 and q: 1 + 3 $\neq$ 4 (3 + 5) < 2 $\rightarrow$ (1 + 3) $\neq$ 4 8 < 2 $\rightarrow$ 4 $\neq$ ...
Let $f,g$ be binary function symbols, $P$ a binary predicate symbol, $c,d$ constant symbols and let $\mathcal{L} := \{f,g;P;c,d\}$. Consider $\mathcal{R}:=\langle\mathbb{R};+,\cdot;<;0,1\rangle$ ...