Independence results for calculi of dependent types

Author(s):  
Thomas Streicher

1992 ◽  
Vol 2 (1) ◽  
pp. 29-54 ◽  
Author(s):  
Thomas Streicher

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.





Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch

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 .



2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi

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.





2006 ◽  
Vol 147 (4) ◽  
pp. 319-335 ◽  
Author(s):  
Shin-ichiro Okada ◽  
Iekata Shiokawa


1966 ◽  
Vol 22 (2) ◽  
pp. 543-546 ◽  
Author(s):  
Frank Haronian ◽  
A. Arthur Sugerman

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.



Author(s):  
Nikhil Swamy ◽  
Juan Chen ◽  
Cédric Fournet ◽  
Pierre-Yves Strub ◽  
Karthikeyan Bhargavan ◽  
...  


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


Sign in / Sign up

Export Citation Format

Share Document