**12**

votes

**0**answers

503 views

### Arguments against Freiling's argument against Continuum Hypothesis

Freiling's axiom of symmetry ($\sf AS$) is known as a justification for falsity of Continuum Hypothesis. Freiling in his 1986 paper, Axioms of symmetry: throwing darts at the real number line, ...

**9**

votes

**0**answers

681 views

### Has anyone pursued Frege's idea of numbers as second-order concepts?

Gottlob Frege was a pivotal figure in the history of mathematical logic. He gave an analysis of numbers that proceeded along roughly the following lines, in his books "The Foundations of Arithmetic" (...

**8**

votes

**0**answers

2k views

### Group Theory, Game Theory, a bit of Philosophy and a post in Tao's blog

I've decided to write this post after reading the incredibly beautiful and highly recomended post by Terence Tao http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-epsilon-...

**5**

votes

**0**answers

672 views

### BGG category everywhere implies generalized Kazhdan-Lusztig formula?

Maybe this question is vague. I am not an expert on what I asked, if I made mistake, please point out.
BGG category was discoverd in Lie algebra setting. One has Verma module $M(\lambda)$, ...

**4**

votes

**0**answers

463 views

### sine and Archimedes' derivation of the area of the circle

The elementary "opposite over hypotenuse" definition of the sine function defines the sine of an angle, not a real number. As discussed in the article "A Circular Argument" [Fred Richman, The College ...

**3**

votes

**0**answers

308 views

### A Question Regarding Boolean-valued Models

What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...

**2**

votes

**0**answers

101 views

### Can the Kunen inconsistency (or the existence of Reinhardt cardinals) be 'properly formulated' in Ackermann set theory?

In their paper "Generalizations of the Kunen Inconsistency" (arXiv:1106.1951v1 [math.LO]10 Jun. 2011), Hamkins, Kirmayer, and Perlmutter write the following:
The first [metamathematical issue--my ...

**2**

votes

**0**answers

114 views

### Some questions regarding an alteration of Grzegorczyk's theory of concatenation, $\operatorname{TC}$

Consider Grzegorczyk's concatenation theory $\operatorname{TC}$, a "weak theory of words over the two letter alphabet $\Sigma=\{a,b\}$" (this from Grzegorczyk and Zdanowski's paper Undecidability and ...

**2**

votes

**0**answers

108 views

### A question regarding an analogue of the Kleene $T$-predicate for Koepke's ordinal computability

Does Koepke's notion of ordinal computability admit an analogue of the Kleene $T$-predicate? If so, is the existence of such a $T$-predicate independent of $ZFC$? Also, if one assumes the existence ...

**2**

votes

**0**answers

73 views

### Which self-reference restrictions can be weakened in probabilstic logic?

This work suggests that there is some generalization of Truth in terms of probability, which can be definable within the logic itself.
Is where any other thorems on self-reference restrictions, which ...

**2**

votes

**0**answers

248 views

### Interpretation of Shannon Entropy Application

Consider a collection of increasing positive integers $\{a_i\}_{i=1}^m$ and the distribution $p_i=\frac{a_i}{\sum_{i=1}^ma_i}$. Let entropy of $\mathcal{A}=\{a_i\}_{i=1}^m$ be given
by $$H(\mathcal{A}...

**2**

votes

**0**answers

142 views

### Is there an universal (dis)similarity measure between two structures?

I'm always wondering is there an universal (dis)similarity measure
between two structures (let's say between two undirected simple
graphs)? I mean, not "the measure with universal parameter that we
...

**2**

votes

**0**answers

455 views

### Single logic foundation vs. multi-logic foundation

Dear all,
I have always wondered why I have never read anything about this topic. My question is, are there are any books or articles covering this subject?
With this topic I mean the philosophical ...

**1**

vote

**0**answers

146 views

### Can Dedekind's 'proof' of the existence of infinite sets be properly formulated and carried out in positive set theory?

This question is related to Mikhail Katz's recent mathoverflow question, "Has Dedekind's proof of the existence of existence of infinite sets been analyzed by historians?". Dedekind's 'proof' seems (...

**1**

vote

**0**answers

98 views

### Can Basic Law $V$ be derived from Leibniz's Law in Second-Order Logic without comprehension principles?

Consider Basic Law $V$:
$\hat x$$F$($x$)=$\hat x$$G$($x$)$\equiv$($\forall$$x$)($F$$x$$\equiv$$G$$x$)
At first glance, it seems to have the same form as Leibniz's law
$x$=$y$$\equiv$($\forall$$F$)($...

**1**

vote

**0**answers

110 views

### A Question Regarding Productive Sets in the Koepke-Koerwien System SO (Sets of Ordinals)

In their paper "The Theory of Sets of Ordinals" (arXiv), Koepke and Koerwien propose a theory SO axiomatizing the class of sets of ordinals in a model of ZFC and show that SO and ZFC are bi-...

**1**

vote

**0**answers

191 views

### A question regarding Koepke' s Ordinal Computability in HOD

Consider the following theorem of Koepke-Koerwien-Siders:
"A set x of ordinals is ordinal computable [either by ordinal Turing machines or ordinal register machines--my comment] if and only if it is ...

**0**

votes

**0**answers

110 views

### Geometric interpretation of table with permutations and inversions

Let $T(n,k)$ is the number of permutations of numbers $1, ..., n$ and each of the permutations has $k$ inversions. We can consider a table for $T(n,k)$ for some $n$ and $k$. For eg.
$n=1,...,6$, $k=1,....