All Questions
1,460 questions with no upvoted or accepted answers
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About a weakening of "union axiom" on ZF set theory
About the axiom of union, from the naive set theory is very natural understand the concept of union (as well others Boolean operation) between the subset os a fixed base set X, this is because $X$ is ...
- 4,165
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179
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semigroup actions of groups on regular rooted trees
If $G$ is a group which has a semigroup action on a regular rooted tree via prefix-preserving, continuous transformations (I give the tree the path metric), what kinds of algebraic restrictions can we ...
- 125
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94
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Relation between properties of functions/sets and Grzegorczyk's hierarchy
I know for example that the first level of the Grzegorczyk hierarchy contains the functions which enumerate the c.e sets and that it has an interesting relation to the provably total functions in ...
- 893
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2
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638
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Peano axioms— mathematical induction and other axioms
The Peano axioms of $\Bbb N$ are:
$1 \in \Bbb N$, i.e. $\Bbb N$ is not empty and contains an element denoted by $1$.
Every natural number has a successor, i.e. $\forall n\in\Bbb N, \exists!s(n)\in\...
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How to prove completness of my axioms for Wumpus world game
I have an implementation of Wumpus world game with some specific rules. Basically, you are an agent which does not see adjacent tiles. There are pits and exactly one wumpus. Moving into pit or tile ...
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Can having no more than countably many classes, be inferred from, having every class being countable?
In a theory having proper classes it won't be that easy to phrase how many classes we have in comparison to the number of elements of some class. Here, I'll adopt the following method:
We'd say that: ...
- 11.3k
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Which arithmetic\set theory is synonymous with this theory?
$\textbf{Logic:}$ Mono-sorted first order logic with equality.
$\textbf{Extralogical Primitives: } <, \in$
Define: $x > y \iff y < x$
Define: $x \leq y \iff x < y \lor x=y$
$ \textbf{...
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Can ZFC be interpreted in this infinitary logic theory?
Working in language $\mathcal L_{\Omega^+,\Omega^+}$ where $\Omega$ is the first strongly inaccessible cardinal. If we add a primitive partial $\Omega$-ary function $F$ and a primitive constant $\...
- 11.3k
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140
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About the definitions of well-foundedness in this extension of NFU that interprets ZFC?
Lets see how the world of sets could look like from the perspective of $\sf NFU$. So, here we work within the first order language of set theory, with the following extra-logical axioms:
1. Quine atom:...
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Can Cardinality Theory capture ZFC?
Cardinality Theory "CT" is a theory of sets of cardinals and links between them, only sets of cardinals can be assigned cardinalities. The links are unordered edges linking cardinals, they ...
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