Logic List Mailing Archive

Thanases Pheidas (1958–2023)

Thanases Pheidas (1958–2023)

   (from the ASL Newsletter)

Prof. Thanases Pheidas, a pillar of the community around Hilbert’s Tenth Problem (H10), passed away unexpectedly on March 27, 2023.

Born on February 18, 1958 in Athens, Greece, Thanases grew up under the Greek military dictatorship, and his views were influenced by his family’s past in the resistance against the Nazi occupation. He graduated from the University of Patras in 1981 with a bachelor’s degree in mathematics and received his Ph.D. from Purdue University in 1985 under the supervision of Leonard Lipshitz. After 1991 he spent the rest of his career in his homeland, at the University of Crete, Heraklion, making frequent visits to the rest of Europe, the USA, and Chile, where his contributions made an important impact.

Thanases had a wide variety of mathematical interests. His Ph.D. thesis proved that a polynomial ring over a field has a decidable existential theory (over the language of addition, divisibility and a variable) just if the existential theory of the field is decidable. Weak Arithmetic held his attention throughout his career: with K. Zahidi, he worked on addition and the Frobenius map for polynomial rings, proving model completeness, while in joint work with X. Vidaux, he solved B¨uchi’s problem and some analogues over rings of functions. An unexpected application led to joint work with H. Pasten and Vidaux that achieved a uniform definition of ps-powers across function fields of a fixed genus, as the characteristic p 
> 0 varies. These researchers also added results concerning Rubel’s
language, with a predicate for the non-constant functions rather than constants for the variables.

Thanases’s best-known works involved undecidability of rings of functions over the ring language, sometimes with some natural additional symbols. 
His seminal 1991 paper in Inventiones Mathematicae proved that H10 is undecidable for rational function fields over finite fields of odd characteristic. He also established the unde- cidability of the first order theory of every rational function field of characteristic ≥ 5, even when the base field is algebraically closed, which had been a major obstacle. At about the same time as A. Shlapentokh and C.R. Videla, he proved that H10 is undecidable for the ring of integers OK when the number field K has exactly two complex (non-real) conjugate embeddings. In the early 2000’s a series of works by Poonen, Cornelissen–Pheidas– Zahidi, and Shlapentokh gave new life to H10, leading to a plethora of advances. 
Additionally, Thanases made substantial contributions to the analogue of
H10 for the ring of complex entire functions.

Thanases was a full person with a deep sense of duty, natural and transparent and always generous in sharing his research ideas and wisdom. 
He connected easily with people, regardless of their backgrounds, occupations or age. He had eclectic tastes and a wide range of interests, including music, singing and playing the guitar, dancing (especially tango), chess, swimming (literally anywhere), sailing, and hiking. 
Inspired by the ancient Greek tradition, he loved doing mathematics while walking.

Thanases is survived by his wife Elisabeth, daughter Danae, two sisters, two granddaughters, and his former wife Renia. His knowledge, abilities, kindness and generosity will be missed by many.
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