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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Prof. Antonio Di Nola, Department of Mathematics, University of Salerno, Italy

Inviter:  
Title:
Infinitary Riesz Logic: a logical approach to Functional Analysis
Time & Venue:
2017.10.7 9:30-10:30 N205
Abstract:
Rieszz Spaces have had a predominant position in the development of functional analysis over ordered structures. They have a widespread of applications related to lattice-ordered vec- tor spaces (vector lattices) and complete normed vector lattices (Banach lattices). Not very known is the role that vector lattices play in logic. Given any positive element u of a riesz Space the interva l[0, u] can be endowed with a stucture of Riesz MV-algebra. These structures have been defined in the setting of Lukasiewicz logic, as expansion of MValgebras the standard semantics of the infinite valued Lukasiewicz logic. It is proved that Riesz MV-algebras are categorical equivalent to Riesz Spaces with a strong unit. Henceforth, vector lattices and logic are closely related. Many results from the theory of Riesz Spaces have facilitated the growth of Lukasiewicz logic and MV-algebras and we will show how Lukasiewicz logic could be an important tool in functional analysis, via Riesz MV-algebras.
 

 

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