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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 ...
mahu's user avatar
  • 53
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 ...
Ethan Splaver's user avatar
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 ...
Dino Rossegger's user avatar
32 votes
9 answers
5k views

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. ...
Joel David Hamkins's user avatar
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 ...
mathymathy's user avatar