Algebrai logika; relativitáselmélet logikai struktúrájának vizsgálata = Algebraic logic; investigating the logical structure of relativity theory

Gödel, Einstein és Tarski hagyományait kívánjuk folytatni, elmélyítve a Gödel-Einstein együttműködés eredményeit is, és folytatva Tarski tudományegyesítési programmját. Ismert, hogy a logika és a matematika modern megalapozása Gödel és Tarski úttörő munkásságára vezethető vissza. Kevésbbé ismert, hogy Gödel 1948-tól majdnem élete végéig Einsteinnel szorosan együttműködve relativitáselméleten dolgozott, ahol ugyanolyan meghökkentő új horizontokat tárt fel mint logikában, és hogy Gödel relativitáselméleti gondolatai folytatásaként fogható fel a forgó fekete lyukak mai elmélete. Ezen előzmények folytatása a jelen projektum, mely Tarskival és munkatársaival való személyes együttműködés (pl. közös könyv) keretében kezdődött. Az alapgondolat a logika, algebra, geometria, téridőelmélet és relativitáselmélet egységben való művelése. Eredményeinkből egy példa: Nagy, lassan forgó fekete lyukakról bizonyítottuk, hogy a belsejében létrejövő un. zárt időszerű görbe (időhurok) létrejöttére vonatkozó szokásos irodalmi magyarázatok tévesek. Nem az un. drag effect (mozgó anyag magával vonszolja a téridőt) okozza a zárt görbéket, hanem egy egészen más jellegű hatás: a fénykúpok kinyílása a forgással ellentétes irányban. Az eredmény a General Relativity and Gravitation című folyóiratban jelenik meg. | The reported project intends to continue traditions of Gödel, Einstein and Tarski continuing the spirit of the Gödel-Einstein collaboration and pursuing Tarski's programme for unifying science. Modern logic and meta-mathematics was created (basically) by Gödel and Tarski. It is less well known that beginning with 1948 Gödel spent much time with Einstein and worked on relativity theory. Of course, he remained a logician in spirit. Gödel obtained fundamental breakthroughs in relativity like his ones in logic and foundations. The theory of general relativistic spacetimes not admitting a global Time was initiated by Gödel, and came to full blossom during the renaissance of black hole physics during the last 25 years. The present project was originally started in personal cooperation with Tarski and his collaborators. The idea is to study logic, algebra, geometry, spacetime theory and relativity in a strong unity. A sample result of ours: We proved about big, slowly rotating black holes that the usual explanation in the literature of why such black holes contain a closed timelike curve (CTC) is flawed. Namely, it is not the gravitational frame dragging effect which creates CTCs, instead, there is a completely different kind of effect in action there: light cones open up in the direction opposite to that of the rotation of the source and this goes on to such an extreme extent that CTCs are created. Our paper on this appears in the journal General Relativity and Gravitation

Chiral high-performance liquid and supercritical fluid chromatographic enantioseparations of limonene-based bicyclic aminoalcohols and aminodiols on polysaccharide chiral stationary phases

Chirality is extremely important for the modern pharmaceutical industry since many drug compounds are chiral molecules whose stereoisomers usually possess various toxicological and pharmacological properties. One of the enantiomers (eutomer) have the desired pharmacological activity, while the other isomer (distomer) is inactive or in worst cases some undesirable effects or even toxic effect can also be produced. The investigated compounds were limonene-based bicyclic 1,3-aminoalcohols and 1,3,5- and 1,3,6-aminodiols. In recent years, these compounds have been intensively investigated due to their potential biological activity and their benefits in synthetic chemistry. Aminoalcohols and aminodiols are known to be outstanding building blocks for the synthesis of remarkable heterocyclic compounds. Aminodiol-based nucleoside analogs possess noteworthy antitumor or antiviral activity [1]. The synthesis of new, limonene-based chiral bicyclic 1,3- aminoalcohols and aminodiols from commercially available starting materials have recently been reported [2]. As a result of the pharmaceutical and biological activity of chiral 1,3-aminoalcohols and aminodiols, it is very important to have at hand enantioselective analytical methods for the identification and separation of these compounds. Enantioseparations of limonene-based bicyclic 1,3-aminoalcohols and 1,3,5- and 1,3,6-aminodiols were carried out with highperformance liquid chromatographic and supercritical fluid chromatographic (SFC) methods on commercial polysaccharide-based chiral stationary phases. The effects of the mobile phase composition, the nature and concentration of the alcohol additive, the temperature and the structures of the studied analytes on the separations were investigated in the normal phase and SFC mode. The elution sequence was determined in all cases. The separations of the stereoisomers of the investigated analytes were optimized in both chromatographic modes