# 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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### What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
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### How to prove this logical equivalence using different laws?

Prove that $﹁p → (q→r)$ and $q → (p∨r)$ are logically equivalent using different laws. this is my answer: $﹁p → (q→r) = q → (p∨r)$ $(q→r) = ﹁q∨r$ implication equivalence $﹁p → (q→r) = p∨(﹁q∨r)$ ...
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### What is the name of a “basis” in Boolean algebras

So, a basis in linear algebra is the smallest set which generates a particular vector space. (More formally, a subset of the vector space which is linearly independent and spans the vector space) Is ...
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### Which rules of inference does Suppes use?

I'm reading Axiomatic Set Theory by Suppes, and I'm having a bit of trouble understanding which rules of inference (logical system) he is using, here's an example (capital letters are used for sets): ...
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### Are all statements about math inherently formal? Can one do math without formal logic? [duplicate]

Are all people who do mathematics applying (whether they know it or not) formal logic? Does every statement someone may make about math, at its core, a formal statement in mathematical logic? ...
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### Difference between a variable and an indeterminate

What are the differences and common points between a variable and an indeterminate ? Is an indeterminate also a variable ? Thank you EDIT : I am not trying to solve anything in particular, it was ...
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### proof verification for natural deduction in propositional logic

Hi I wanted to know if I got the following natural deduction formula correct. ...
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### Characterizing coding with automorphisms

I am attempting the following exercise from chapter 5 of Van den Dries' notes "Introduction to Model-Theoretic Stability". I suspect the exercise shouldn't be too difficult but I've become pretty ...
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### Alternate form of Modus tollens applicable?

The definition states that not(q) p--> q ---------- not(p) Is the following form is also true? ...
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### Can multiplication and division be treated as logical operations?

A few of my friends and I were playing around with math (more specifically, why (-1)(-1)=1) and we figured out that multiplication (with regards to signs) was an "nxor" operation (I.E. If we treat "1" ...
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### Translate “If I would not exist if I will travel back in time, then I will not travel back in time” into predicate logic.

"If I would not exist if I will travel back in time, then I will not travel back in time" Translating the conditionals using ⊃ and 'I do not exist' as 'I am not something', find a tautologous form ...
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### Counting Possible Ways to Score in a Basketball Game

In a basketball game, a goal is worth 1,2, or 3 points. Given the score n of a team at the end of the game, we are interested in the possible ways the score n can be achieved. Write a function ...
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### How can I write a DNF to CNF form?

How can I have write (p∧q) ∨ (¬p ∧ ¬q), which is the equivalent for (p<->q), in conjunctive normal form (CNF)? In general, am I allowed to do (p ∨ (¬p ∧ ¬q)) ∧ (q ∨ (¬p ∧ ¬q)) ??
### Showing that $(p(x)\rightarrow q(x)) \leftrightarrow (\neg q(x) \rightarrow \neg p(x))$ is a valid $\mathcal{L}$-formula
If $\mathcal{L}=\{p,q\}$ with $p,q \in \mathcal{P}_1$, would showing that $(p(x)\rightarrow q(x))$ and $(\neg q(x) \rightarrow \neg p(x))$ have the same truth table prove that \$(p(x)\rightarrow q(x)) ...