Formulation of the modular Hilbert algebra

1970 ◽  
pp. 52-57
Author(s):  
M. Takesaki
Keyword(s):  
Hilbert Algebra

The Belluce-lattice associated with a bounded Hilbert algebra

2015 ◽  
Vol 19 (11) ◽  
pp. 3031-3042
Author(s):  
Dumitru Buşneag ◽  
Dana Piciu
Keyword(s):  
Hilbert Algebra

scholarly journals Square-integrable representations of non-unimodular groups

1976 ◽  
Vol 15 (1) ◽  
pp. 1-12 ◽  
Author(s):  
A.L. Carey
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Hilbert Algebra ◽  
Technical Tool ◽  
Integrable Representation ◽  
Hilbert Algebras ◽  
Orthogonality Relations ◽  
Square Integrable Representation ◽  
Main Technical Tool

In the last three years a number of people have investigated the orthogonality relations for square integrable representations of non-unimodular groups, extending the known results for the unimodular case. The results are stated in the language of left (or generalized) Hilbert algebras. This paper is devoted to proving the orthogonality relations without recourse to left Hilbert algebra techniques. Our main technical tool is to realise the square integrable representation in question in a reproducing kernel Hilbert space.

David Hilbert: Algebra and Axiomatics

2004 ◽  
pp. 137-182 ◽  
Author(s):  
Leo Corry
Keyword(s):  
Hilbert Algebra ◽  
David Hilbert

scholarly journals Relation between right and left involutions of a Hilbert algebra

1988 ◽  
Vol 102 (1) ◽  
pp. 57-57
Author(s):  
P. P. Saworotnow
Keyword(s):  
Hilbert Algebra

scholarly journals On the free frontal implicative semilattice extension of a frontal Hilbert algebra

2019 ◽  
Vol 23 (21) ◽  
pp. 10635-10648 ◽  
Author(s):  
Ramon Jansana ◽  
Hernán J. San Martín
Keyword(s):  
Hilbert Algebra

Implicational formulas in intuitionistic logic

1974 ◽  
Vol 39 (4) ◽  
pp. 661-664 ◽  
Author(s):  
Alasdair Urquhart
Keyword(s):  
Propositional Calculus ◽  
Modus Ponens ◽  
Equivalence Classes ◽  
Alternative Proof ◽  
Hilbert Algebra ◽  
Hilbert Algebras ◽  
Free Generators ◽  
Finite Set ◽  
Image Position ◽  
The Right

In [1] Diego showed that there are only finitely many nonequivalent formulas in n variables in the positive implicational propositional calculus P. He also gave a recursive construction of the corresponding algebra of formulas, the free Hilbert algebra In on n free generators. In the present paper we give an alternative proof of the finiteness of In, and another construction of free Hilbert algebras, yielding a normal form for implicational formulas. The main new result is that In is built up from n copies of a finite Boolean algebra. The proofs use Kripke models [2] rather than the algebraic techniques of [1].Let V be a finite set of propositional variables, and let F(V) be the set of all formulas built up from V ⋃ {t} using → alone. The algebra defined on the equivalence classes , by settingis a free Hilbert algebra I(V) on the free generators . A set T ⊆ F(V) is a theory if ⊦pA implies A ∈ T, and T is closed under modus ponens. For T a theory, T[A] is the theory {B ∣ A → B ∈ T}. A theory T is p-prime, where p ∈ V, if p ∉ T and, for any A ∈ F(V), A ∈ T or A → p ∈ T. A theory is prime if it is p-prime for some p. Pp(V) denotes the set of p-prime theories in F(V), P(V) the set of prime theories. T ∈ P(V) is minimal if there is no theory in P(V) strictly contained in T. Where X = {A1, …, An} is a finite set of formulas, let X → B be A1 →····→·An → B (ϕ → B is B). A formula A is a p-formula if p is the right-most variable occurring in A, i.e. if A is of the form X → p.

Stonean Hilbert algebra

2015 ◽  
Vol 30 (1) ◽  
pp. 485-492 ◽  
Author(s):  
Ali Soleimani Nasab ◽  
Arsham Borumand Saeid
Keyword(s):  
Hilbert Algebra

Semi maximal filter in Hilbert algebra

2015 ◽  
Vol 30 (1) ◽  
pp. 7-15 ◽  
Author(s):  
Ali Soleimani Nasab ◽  
Arsham Borumand Saeid
Keyword(s):  
Hilbert Algebra ◽  
Maximal Filter

scholarly journals Positive integrable elements relative to a left Hilbert algebra

1973 ◽  
Vol 13 (4) ◽  
pp. 390-409 ◽  
Author(s):  
John Phillips
Keyword(s):  
Hilbert Algebra
Sign in / Sign up

Export Citation Format

Share Document