NameLara Martín, Francisco Félix
DepartmentCiencias de la Computación e Inteligencia Artificial
Knowledge areaCiencia de la Computación e Inteligencia Artificial
Professional categoryProfesor Titular de Universidad
E-mailRequest
           
  • No. publications

    24

  • No. visits

    3231

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    8821


 

Final Degree Project
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Teoría de conjuntos finitos

Barea Marín, Pablo Luis; Lara Martín, Francisco Félix (2023)
La Teoría de Conjuntos es un área del conocimiento comprendida entre la Lógica y las Matemáticas dedicada a la fundamentación ...
Final Degree Project
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La lógica de la demostrabilidad

Ortiz Morales, Samuel; Lara Martín, Francisco Félix (2021)
Our main goal in this work is the study of the arithmetical completeness theorem for GL (presented for first time by Solovay ...
Final Degree Project
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El teorema de Goodstein

Muñoz Sánchez, Araceli; Lara Martín, Francisco Félix (2021)
Este trabajo se centra en el Teorema de Goodstein. El primer objetivo será demostrarlo. Para ello, debemos introducir al ...
Final Degree Project
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El Axioma de Determinación

Ferre Luque, Antonio; Cordón Franco, Andrés; Lara Martín, Francisco Félix (2020)
The aim of this work is to study the consequences of assuming the axiom of determinacy regarding perfect set property, ...
Final Degree Project
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Fundamentos de IA para el ajedrez

Portillo Raya, Alberto; Lara Martín, Francisco Félix; Sancho Caparrini, Fernando (2019)
El presente trabajo tiene como objetivo la introducción y desarrollo de los fundamentos teóricos de algunas técnicas ...
Final Degree Project
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Lógica minimal, intuicionista y clásica

Sierra Rodríguez, Patricia; Lara Martín, Francisco Félix (2018)
The classical systems traditionally accepted within formal mathematical reasoning coexists with other branches of logic ...
Article
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Predicativity through Transfinite Reflection

Cordón Franco, Andrés; Fernández Duque, David; Joosten, Joost J.; Lara Martín, Francisco Félix (The Association for Symbolic Logic, 2017)
Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use as a formalization of “φ is provable ...
Final Degree Project
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Complejidad computacional y álgebra de funciones

Romero González, Alberto; Lara Martín, Francisco Félix (2016)
Usually, computational complexity classes are given explicitly using computation models and certain restrictions on available ...
Article
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Existentially Closed Models in the Framework of Arithmetic

Adamowicz, Zofia; Cordón Franco, Andrés; Lara Martín, Francisco Félix (The Association for Symbolic Logic, 2016)
We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. ...
Article
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On axiom schemes for T-provably Δ1 formulas

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Springer, 2014)
This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and ...
Article
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Local induction and provably total computable functions

Cordón Franco, Andrés; Lara Martín, Francisco Félix (Elsevier, 2014)
Let I¦− 2 denote the fragment of Peano Arithmetic obtained by restricting the induction scheme to parameter free ¦2 formulas. ...
Article
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On the Optimality of Conservation Results for Local Reflection in Arithmetic

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Association for Symbolic Logic, 2013)
Let T be a recursively enumerable theory extending Elementary Arithmetic EA. L. D. Beklemishev proved that the Σ2 local ...
Presentation
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Local Induction and Provably Total Computable Functions: A Case Study

Cordón Franco, Andrés; Lara Martín, Francisco Félix (Springer, 2012)
Let IΠ−2 denote the fragment of Peano Arithmetic obtained by restricting the induction scheme to parameter free Π2 ...
Article
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A note on parameter free Π1-induction and restricted exponentiation

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Wiley, 2011)
We characterize the sets of all Π2 and all $\mathcal {B}(\Sigma _{1})$equation image (= Boolean combinations of Σ1) theorems ...
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Existentially Closed Models and Conservation Results in Bounded Arithmetic

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Oxford Academic, 2009)
We develop model-theoretic techniques to obtain conservation results for first order Bounded Arithmetic theories, based ...
Presentation
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On Rules and Parameter Free Systems in Bounded Arithmetic

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Springer, 2007)
We present model–theoretic techniques to obtain conservation results for first order bounded arithmetic theories, based on a hierarchical version of the well known notion of an existentially closed model.
Article
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A Note on Σ₁-Maximal Models

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Association for Symbolic Logic, 2007)
Let T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of ...
Article
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Envelopes, indicators and conservativeness

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Wiley, 2006)
A well known theorem proved (independently) by J. Paris and H. Friedman states that BΣn +1 (the fragment of Arithmetic ...
Article
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Fragments of Arithmetic and true sentences

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Wiley, 2005)
By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the ¦n+1–sentences true in the standard model is ...
Article
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Induction, minimization and collection for Δ n+1 (T)–formulas

Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Springer, 2004)
For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained ...
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On the quantifier complexity of Δ n+1 (T)– induction

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Springer, 2004)
In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity ...
Presentation
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Provably Total Primitive Recursive Functions: Theories with Induction

Cordón Franco, Andrés; Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Springer, 2004)
A natural example of a function algebra is R (T), the class of provably total computable functions (p.t.c.f.) of a theory ...
Article
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Some Results on LΔ n+1

Fernández Margarit, Alejandro; Lara Martín, Francisco Félix (Wiley, 2001)
We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.
PhD Thesis
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Inducción y recursión las teorías IDelta n+1(T) /

Lara Martín, Francisco Félix; Fernández Margarit, Alejandro (1999)
En este trabajo se realiza un análisis de la conjetura de Friedman-Paris, acerca de la equivalencia entre los fragmentos ...