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Results tagged with lo.logic
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user 82843
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
2
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1
answer
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On the Actual Potential of Virtual Large Cardinals
Virtual large cardinals belong to a relatively new breed of strong axioms of infinity. They often appear as statements of the following form:
Definition. Suppose $A$ is a large cardinal property c …
8
votes
2
answers
308
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Does fast function forcing really have $\kappa$-Knaster property?
I ran into a claim concerning Woodin's fast function forcing in the following paper of Apter and Cummings which sounds no right to me:
A. Apter, J. Cummings, Blowing up the power set of the least meas …
5
votes
1
answer
673
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What are examples of non-equivalent virtualizations of a large cardinal?
This is a follow up to my previous question concerning virtual large cardinals, that are generally weaker axioms of infinity obtained from ordinary large cardinals through the so-called virtualization …
11
votes
2
answers
678
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On Applications of Forcing in Domain Theory
An interesting feature of domain theory is to use partial orders in order to provide a mathematical model for the computational approximation in a potentially infinite computational process (e.g. comp …
24
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1
answer
1k
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Forcing and Family Contentions: Who wins the disputes?
The famous game-theoretic couple, Alice & Bob, live in the set-theoretic universe, $V$, a model of $ZFC$. Just like many other couples they sometimes argue over a statement, $\sigma$, expressible in t …
10
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1
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1k
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The Tall Tale of Terminating Transfinite Towers
The transfinite tower of iterative automorphisms of a group $G$ is simply definied to be the following chain of the groups where $G_{\alpha+1}=Aut(G_{\alpha})$ for each ordinal $\alpha$ and the direct …
9
votes
1
answer
595
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On the Large Cardinal Strength of Normal Moore Space Conjecture
In his seminal 1937 paper, Jones [1] proved the following result about Moore spaces:
Theorem. (Jones) If $2^{\aleph_0}<2^{\aleph_1}$ then all separable normal Moore spaces are metrizable.
Then h …
10
votes
0
answers
437
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On the Number of Parallel Automorphism Lines
Given a group $G$, one can define the transfinite line of iterative automorphisms of $G$ to be the following chain of the groups where $G_{\alpha+1}=Aut(G_{\alpha})$ for each ordinal $\alpha$ and the …
18
votes
1
answer
2k
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What is the modal logic of outer multiverse?
The mathematical multiverse could be viewed as a gigantic Kripke model with models of $ZFC$ as possible worlds connected to each other via a certain accessibility relation.
The modal logic associated …
35
votes
7
answers
4k
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Paradoxical Mathematical Objects Pending for Construction [duplicate]
The possible properties and applications of some mathematical objects have been described far before their rigorous mathematical definition. Some of them even had a seemingly paradoxical description w …
113
votes
11
answers
17k
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On mathematical arguments against Quantum computing
Quantum computing is a very active and rapidly expanding field of research. Many companies and research institutes are spending a lot on this futuristic and potentially game-changing technology. Some …
31
votes
2
answers
3k
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Mathematical Evidence Backing $|\mathbb{R}|=\aleph_2$
The "true" size of the real line, $\mathbb{R}$, has been the subject of Hilbert's first problem. Due to the Goedel and Cohen's work on the inner and outer models of $\text{ZFC}$, it turned out to be u …
39
votes
4
answers
6k
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On critical reviews of Hawking's lecture "Gödel and the end of the universe"
The search for a neat Theory of Everything (ToE) which unifies the entire set of fundamental forces of the universe (as well as the rules which govern dark energy, dark matter and anti-matter realms) …
31
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8
answers
3k
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On independence and large cardinal strength of physical statements
The present post is intended to tackle the possible interactions of two bizarre realms of extremely large and extremely small creatures, namely large cardinals and quantum physics.
Maybe after all tho …
70
votes
6
answers
8k
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The logic of Buddha: a formal approach
Buddhist logic is a branch of Indian logic (see also Nyaya), one of the three original traditions of logic, alongside the Greek and the Chinese logic. It seems Buddha himself used some of the features …