All Questions
5 questions
32
votes
9
answers
5k
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How many groups of size at most n are there? What is the asymptotic growth rate? And what of rings, fields, graphs, partial orders, etc.?
Question. How many (isomorphism types of) finite groups of size at most n are there? What is the asymptotic growth rate? And the same question for rings,
fields, graphs, partial orders, etc.
...
8
votes
1
answer
1k
views
Wikipedia article on forbidden graph substructures
I apologies if this is too trivial a question or if I am over complicating anything here. But I was hoping for some clarification in an article I was reading about forbidden graph substructures on ...
4
votes
1
answer
154
views
Kruskal's tree theorem and $\Pi_1$ sentences of linear orderings with finitely many constants
In their paper "Theories with recursive models" [1] Lerman and Schmerl used a version of Kruskal's tree theorem about finite n-augmented trees.
An n-augmented tree is a tree T together with $n$ unary ...
3
votes
3
answers
266
views
Name for "lower/upper bounds" of arbitrary relations?
Given a partial order $R_{\leq}$ over a set $D$, the set of upper bounds under $R$ of a subset $S$ of $D$ is commonly defined as $\{ y \in D | \ \forall x\in S, x R y \}$.
(The set of lower bounds of ...
3
votes
0
answers
127
views
A class of Kripke frames which preserves validity
The background of our discussion is intuitionistic logic, i.e. the following definitions are intuitionistic Kripke frame.
For $1\leq s\leq n-2$, the frame $\mathcal{C}_n(s)$ denotes the frame which is ...