Emanuele Frittaion

Dipartimento di Scienze Matematiche, Informatiche e Fisiche - DMIF - Università di Udine.

Assegnista di Ricerca. Project: "Analisi della forza in teoria degli insiemi, in analisi computabile e nell'aritmetica del second'ordine"  SSD: MAT/01.  Responsabile scientifico: Alberto Giulio Marcone. (Assegno di ricerca cofinanziato a valere sulle risorse del progetto PRIN 2022 - Prot. n. 2022TECZJA).

Research 

• Reverse mathematics.

• Proof theory of arithmetic.

• Intuitionistic logic.

• Constructive set theory.

Publications

• Relations between higher order arithmetic and set theory. (w/ Giorgio Genovesi). In progress. 

• Iterating reflection over intuitionistic arithmetic. Submitted. 

• Peano arithmetic, games and descent recursion. Annals of Pure and Applied Logic, 176(4) (2025) [pdf] [DOI]

• Choice and independence of premise rules in intuitionistic set theory (w/ Takako Nemoto and Michael Rathjen). Annals of Pure and Applied Logic, 174(9) (2023) [pdf] [DOI]

• Extensional realizability and choice for dependent types in intuitionistic set theory. The Journal of Symbolic Logic, 88(3): 1138-1169 (2023) [pdf] [DOI]   

• A note on fragments of uniform reflection in second order arithmetic. The Bulletin of Symbolic Logic, 28(3): 451-465 (2022) [pdf] [DOI]

• Extensional realizability for intuitionistic set theory (w/ Michael Rathjen). Journal of Logic and Computation, 31(2): 630-653 (2021) [pdf] [DOI]

• Completeness of the primitive recursive ω-rule. Archive for Mathematical Logic, 59: 715-731 (2020) [pdf] [DOI]

• On Goodman realizability. Notre Dame Journal of Formal Logic, 60(3): 523-550 (2019) [pdf] [DOI]

• The strength of SCT soundness (w/ Florian Pelupessy, Silvia Steila, and Keita Yokoyama). Journal of Logic and Computation, 28(6): 1217-1242 (2018) [pdf] [DOI

• Brown's lemma in second-order arithmetic. Fundamenta Mathematicae, 238: 269-283 (2017) [pdf] [DOI]

• Coloring the rationals in reverse mathematics (w/ Ludovic Patey). Computability, 6(4): 319-331 (2017) [pdf] [DOI]

• The strength of the SCT criterion (w/ Silvia Steila and Keita Yokoyama). Theory and Applications of Models of Computation 2017. LNCS 10185 Springer: 260-273 (2017) [pdf] [DOI]

• Reverse mathematics, well-quasi-orders, and Noetherian spaces (w/ Matt Hendtlass, Alberto Marcone, Paul Shafer, Jeroen Van der Meeren). Archive for Mathematical Logic, 55(3): 431-459 (2016) [pdf] [DOI]

• Reverse Mathematics and initial intervals (w/ Alberto Marcone). Annals of Pure and Applied Logic, 165(3): 858-879 (2014) [pdf] [DOI]

• Linear extensions of partial orders and reverse mathematics (w/ Alberto Marcone). Mathematical Logic Quarterly, 58(6): 417-423 (2012) [pdf] [DOI]

Thesis

• Reverse Mathematics and partial orders (Advisor: Alberto Marcone). PhD Thesis, University of Udine (2014) [pdf] [DOI] 

• Abstract of the thesis. The Bulletin of Symbolic Logic, 24 (2): 196-96 (2018) [DOI] 

Short cv

I received my PhD in March 2014 from the University of Udine, Italy, under the supervision of Professor Alberto Marcone.

From 2014 to 2016, I was a JSPS Postdoctoral Fellow in the Department of Mathematics at Tohoku University, Japan, under the guidance of Professor Kazuyuki Tanaka.

From 2016 to 2018, I was a Postdoctoral Researcher in the Department of Mathematics at the University of Lisbon, Portugal, under the guidance of Professor Fernando Ferreira.

From 2018 to 2020, I was a Research Fellow in the School of Mathematics at the University of Leeds, UK, under the guidance of Professor Michael Rathjen and Dr Paul Shafer.

From 2020 to 2022, I was a recipient of a Humboldt Research Fellowship for Postdoctoral Researchers in the Department of Mathematics at TU Darmstadt, Germany, under the guidance of Professor Ulrich Kohlenbach. 

From 2022 to 2024, I was a Research Fellow in the School of Mathematics of the University of Leeds, UK. 

Since 2024, I am an Assegnista di Ricerca in the Department of Mathematics of the University of Udine.