Luonnollisten lukujen joukon määriteltävyys funktioalgebroissa

Let X be a topological space and K the real algebra of the reals, the complex numbers, the quaternions, or the octonions. The functions form X to K form an algebra T(X,K) with pointwise addition and multiplication. We study first-order definability of the constant function set N' corresponding to the set of the naturals in certain subalgebras of T(X,K). In the vocabulary the symbols Constant, +, *, 0', and 1' are used, where Constant denotes the predicate defining the constants, and 0' and 1' denote the constant functions with values 0 and 1 respectively. The most important result is the following. Let X be a topological space, K the real algebra of the reals, the compelex numbers, the quaternions, or the octonions, and R a subalgebra of the algebra of all functions from X to K containing all constants. Then N' is definable in , if at least one of the following conditions is true. (1) The algebra R is a subalgebra of the algebra of all continuous functions containing a piecewise open mapping from X to K. (2) The space X is sigma-compact, and R is a subalgebra of the algebra of all continuous functions containing a function whose range contains a nonempty open set of K. (3) The algebra K is the set of reals or the complex numbers, and R contains a piecewise open mapping from X to K and does not contain an everywhere unbounded function. (4) The algebra R contains a piecewise open mapping from X to the set of the reals and function whose range contains a nonempty open subset of K. Furthermore R does not contain an everywhere unbounded function.

Juutalaisvastaisuus suomalaisissa aikakauslehdissä ja kirjallisuudessa 1918-1944

Anti-Semitism existed in Finland during the whole period covered by this study. The immoral acts associated with Jews in the articles were mostly regarded as universal habits, qualities and/or modes of action, that is, unconnected with any particular Finnish Jew. Researchers have tried to explain anti-Semitism in several ways. The theory of Jews as outsiders has been a popular explanation as well as xenophobia, chimerical anti-Semitism and the socio-economic models. The main sources of this study have been over 400 Finnish periodicals and magazines, literature and text books published between 1918 and 1944. This vast number of magazines includes those of the army and the civil guard, religion, humour and the papers of the Finnish extreme right. One can see a distinct foreign and especially German influence in the subjects and phraseology of Finnish anti-Semitic writings between 1918 and 1944. Several known Finnish anti-Semitic writers had some kind of link with Germany. Some Finnish organisations and societies were openly anti-Semitic during this period. There had been cycles in the activity of anti-Semitic writing in Finland, obvious peaks appearing in 1918 1919, 1929 1931, 1933 1938 and 1942 1944. The reason for the 1918 1919 activity was the civil rights which were granted to the Jews in Finland, and the Russian Bolshevik revolution. The worldwide depression from 1929 to 1932 seem to be the reason for new anti-Semitic writing activity. The rise of National Socialism in Germany and the influence this phenomenon had in Finland was the reason for the peak during 1933 1938. During the continuation war 1942 1944 National Socialist Germany was fighting side-by-side with Finland and their anti-Semitic propaganda found easier access to Finland. Of the 433 magazines, journals and newspapers which were used in this study, 71 or 16.4 per cent had at least one article that can be identified as anti-Semitic; especially the magazines of national socialists and other extreme right parties were making anti-Semitic annotations. There were about 50 people known to have written anti-Semitic articles. At least half of these known writers had studied at the university, including as many as 10 priests. Over and above these, there was an even larger number of people who wrote under a pseudonym. The material used suggested that anti-Semitism was not very popular in Finland between 1918 and 1944. Anti-Semitic articles appeared mostly in the magazines of the extreme right, but their circulation was not very large. A proof of the slight influence of these extreme right anti-Semitic ideas is that, beside the tightening of policy towards Jewish immigrants in 1938 and the handing over of eight of these refugees to Germany in 1942, the official policy of Finland never became anti-Semitic. As was stated before, despite the cycles in the number of writings, there does not appear to have been any noticeable change in public opinion. One must also remember that most Finns had not at that period actually met a Jew. The material used suggests that between 1918 and 1944 the so-called Jewish question was seemingly unimportant for most Finns and their attitude to Jews and Jewishness can be described as neutral.

Stalinismin lyhyt kurssi : Suomalaiset Moskovan Lenin-koulussa 1926-1938

This study of the Finns at the International Lenin School (ILS) reflects history of the Soviet Union during Stalin's era, history of the Communist International (Comintern) as well as history of Finnish communism. The life span of the ILS (1926-1938) matches up with creating and establishing the power structures of Stalinism. Both the ILS and Finnish Communism in the USSR became casualties of the Great Terror (1937-1938). After the WW2, however, the Soviet education was appreciated inside the Communist Party of Finland (CPF). If Finland would have become People's Democracy, the former ILS students would have composed the inner circle of the new "democratic" government. The Finnish teachers of the ILS were leaders of the CPF that was headquartered in Moscow. At the ILS studied in total 141 Finnish communists. The purpose of the ILS was to educate the communist parties' leading stratum of functionaries. They were supposed to internalize current values, methods and discipline of the Bolsheviks. This study evaluates the effects of the total school experience on the Finns that often ended in another total institution in Finland: prison. The curricula of the ILS consisted of theory of Marxism-Leninism, party history, political economics and themes of campaigns of Stalinism. The ILS year included participation in Bolshevik party life and practical work. During summer excursions (praktikas) the students could acquaint themselves with building of socialism in the Soviet Republics. At the ILS, intention to ideological moulding was not hidden. The students were supposed to adopt the Stalinist identity of the professional revolutionaries of the era. The ILS was saturated with ideology and propaganda. This study analyzes especially uses of history as vehicle of ideological standardisation and as instrument of power. Stalin contributed personally to shortcomings of history writing of the communist party. Later he supervised writing of the inclusive handbook of communism, "History of the All-Union Communist Party. Short Course". Special attention will be paid to the effects of Stalin's intervention at the ILS and inside the CPF. The life of the Finns at the ILS and outside the school is described at grass roots. The dividing line between personal and political is analyzed by charting emotional, intimate and bodily experiences of the Finns of the ILS. The fates of the ILS Finns after the studying or teaching period in Moscow are explored in detail. The protagonist among the teachers is Yrjö Sirola that was called "father of the CPF cadres". The Finnish ILS teachers and the formed students that had remained in the USSR were most severely hit by the Great Terror. The Soviet education had most importance in Finland of post WW2 period. The training at the ILS, however, did not contribute to revolution in Finland. The main heading of the study, "A Short Course of Stalinism", crystallises interpretation of the ILS as seat of learning of ideological unity of Stalinism. On the other hand, the title includes a statement of incompleteness of the Stalinist education if the schooling at the ILS had remained in one year.