Independence results for calculi of dependent types

2005 ◽  
pp. 141-154 ◽  
Author(s):  
Thomas Streicher
Keyword(s):  
Dependent Types ◽  
Independence Results

Dependence and independence results for (impredicative) calculi of dependent types

1992 ◽  
Vol 2 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Thomas Streicher
Keyword(s):  
Dependent Types ◽  
Cartesian Closed Category ◽  
Closed Category ◽  
Strong Notion ◽  
Independence Results ◽  
Cartesian Closed ◽  
Categorical Semantics

Based on a categorical semantics for impredicative calculi of dependent types we prove several dependence and independence results. Especially we prove that there exists a model where all usual syntactical concepts can be interpreted with only one exception: in the model the strong sum of a family of propositions indexed over a proposition need not be isomorphic to a proposition again.The method of proof consists of restricting the set of propositions in the well known PERw model due to E. Moggi. The subsets of PERw considered in this paper are inspired by the subset ExpO of PERw introduced by Freyd et al.Finally we show that a weak and a strong notion of sub-locally-cartesian-closed-category coincide under rather mild completeness conditions.

Positively dependent types

2008 ◽  
Author(s):  
Daniel R. Licata ◽  
Robert Harper
Keyword(s):  
Dependent Types

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

Further independence results

1982 ◽  
pp. 388-393
Keyword(s):  
Independence Results

Algebraic Independence Results Related to 〈q, r〉-Number Systems

2006 ◽  
Vol 147 (4) ◽  
pp. 319-335 ◽  
Author(s):  
Shin-ichiro Okada ◽  
Iekata Shiokawa
Keyword(s):  
Algebraic Independence ◽  
Number Systems ◽  
Independence Results

Field Independence and Resistance to Reversal of Perspective

1966 ◽  
Vol 22 (2) ◽  
pp. 543-546 ◽  
Author(s):  
Frank Haronian ◽  
A. Arthur Sugerman
Keyword(s):  
Short Form ◽  
Necker Cube ◽  
Normal Male ◽  
Field Independence ◽  
Embedded Figures Test ◽  
Following Instructions ◽  
Independence Results ◽  
Male University Students ◽  
Rod And Frame Test ◽  
Rod And Frame

The more successful 102 normal male university students were in following instructions to resist fluctuations of the Necker cube, the more field-independently they scored on both Series III of the rod-and-frame test ( r = .28) and on Jackson's short form of the embedded-figures test ( r = .24). Under neutral instructions, the correlations were nil. Results support prior findings that a small but significant portion of the variance of Necker cube fluctuations under instructions to control the rate of shift is related to scores of field independence. Results support Jackson's finding that ability to control the rate of shift is not related to intelligence.

scholarly journals Secure distributed programming with value-dependent types

2011 ◽  
Author(s):  
Nikhil Swamy ◽  
Juan Chen ◽  
Cédric Fournet ◽  
Pierre-Yves Strub ◽  
Karthikeyan Bhargavan ◽  
...  
Keyword(s):  
Distributed Programming ◽  
Dependent Types

Foundations of path-dependent types

2014 ◽  
Vol 49 (10) ◽  
pp. 233-249 ◽  
Author(s):  
Nada Amin ◽  
Tiark Rompf ◽  
Martin Odersky
Keyword(s):  
Dependent Types ◽  
Path Dependent
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